Define a Prime

[Patrick123]

My p cents worth:

p is prime iff the only two factors of p are p and p/p provided
p <> p - p and
p <> p/p

Regards
Patrick

[Mini-Geek]

Originally Posted by Patrick123

My p cents worth:

p is prime iff the only two factors of p are p and p/p provided
p <> p - p and
p <> p/p

Regards
Patrick

Violation.

[Patrick123]

Originally Posted by Mini-Geek

Violation.

Whoops let's rephrase that:

p is prime iff its only factors are p and p/p provided
p <> p - p and
p <> p/p and
p is positive.

Regards
Patrick

[Jushi]

Originally Posted by R.D. Silverman

An integer p is prime if and only if for all A,B, such that A^2 = B^2 mod p,
then A=B mod p or A=-B mod p.

So, 1 and 6 are primes then?

[S485122]

Originally Posted by Jushi

So, 1 and 6 are primes then?

How do you define an equality modulo 1 ?

[Jushi]

Originally Posted by S485122

How do you define an equality modulo 1 ?

Usually, "a = b mod c" means "c divides (b-a)". Then any two integers are equal mod 1, because 1 divides any integer.

[m_f_h]

Originally Posted by S485122

How do you define an equality modulo 1 ?

That's not much worse than equality mod which everyone knows from study of trigonometric functions... "x = y (mod z)" is defined for any number z (including 0, where it gives equality) as he wrotes, or where Z are the integers, i.e. zZ are all numbers of the form zk with k some integer.